When heating up ice, the first thing we need to notice is that the curve is
not a straight line, but has 5 straight segments. Each segment is " ruled
" by a different equation. To calculate the total energy change (delta H)
of a change, calculate the energy of each segment and add them together.

1. In this region we are heating ice. The formula for how energy is needed
is: ΔH= m * ΔT*Cp.

Where ΔH
is the change in energy needed, m is
the mass of ice being warmed or cooled, ΔT
is the temperature change (Ending T- Beginning T), and Cp
is the specific heat of the ice (0.5 cal/g °C)

2. In this region a curious thing happens, the temperature neither goes up or
down, all the heat energy is used in melting or freezing. The formula for how
energy is needed is:ΔH= m * Hf

Where ΔH
is the change in energy needed, m is
the mass of ice melted or the mass of water being frozen, Hfis the heat of fusion of ice (80 cal/g)

3. In this region we are warming water, with no phase change so the equation
is: ΔH= m * ΔT*Cp.

Where ΔH
is the change in energy needed, m is
the mass of ice being warmed or cooled, ΔT
is the temperature change (Ending T- Beginning T), and Cp
is the specific heat of the water (1.0 cal/g °C)

4. In this region another phase change occurs.Water is converted to steam (or
steam to water) without any temperature rise. The formula for how
energy is needed is:ΔH= m * Hv

Where ΔH
is the change in energy needed, m is
the mass of water vaporized or the mass of steam being condensed, Hv
is the heat of vaporization of water (a huge 540 cal/g)

5. In this region we are heating steam. The formula for how energy is needed
is: ΔH= m * ΔT*Cp.

Where ΔH
is the change in energy needed, m is
the mass of steam being warmed or cooled, ΔT
is the temperature change (Ending T- Beginning T), and Cp
is the specific heat of the steam (0.5 cal/g °C)

To solve numerical problems plot the beginning point and ending point on the
graph and break the heating into small segments (up to 5) calculate the energy
change for each step and add them together for the total energy change of the
total "trip". Calculate using only positive numbers and assign a sign
at the very end: left and down represents - calories; up and right is +
calories.

In Mr. K's class we will use calories so we can relate to food calories
(kilocalories). In case you want to relate to the rest of the world though,